This application claims the benefit of a Japanese Patent Application No. 2002-018640 filed Jan. 28, 2002, in the Japanese Patent Office, the disclosure of which is hereby incorporated by reference.
1. Field of the Invention
The present invention generally relates to etalons and external resonance type lasers, and more particularly to an etalon which eliminates a need for a reflection mirror by making a reflected light which is obtained through multiple reflection have a wavelength selection characteristic, and to an external resonance type laser which has a simplified optical system by using such an etalon as a wavelength selection element.
2. Description of the Related Art
When forming an optical transmission system, it is in most cases necessary to use a wavelength selection element having a wavelength selection characteristic. Particularly in the case of a wavelength multiplexing optical transmission system, it is essential to use the wavelength selection element, and various elements based on various operating principles are used as the wavelength selection element. An etalon is one of such elements. The etalon forms two reflection surfaces, and utilizes the multiple reflection between the two reflection surfaces. The etalon is characterized by its simple structure and the capability of being set to have a wavelength selection characteristic in a wide range. But there are demands to further simplify the structure of the etalon and to enable an accurate wavelength selection characteristic to be obtained.
Due to the trend of the number of wavelengths to increase in the wavelength multiplexing optical transmission system, the need for a laser having an accurate oscillation wavelength is increasing, thereby resulting in the development of external resonance type lasers. There are demands to further simplify the structure and to stabilize the oscillation wavelength of the external resonance type lasers.
FIG. 1 is a diagram showing a basic structure of a conventional etalon.
As shown in FIG. 1, two reflection surfaces 1 and 2 having a certain reflectivity confront each other. A solid or gas having a light transmitting characteristic is disposed in a gap between the two reflection surfaces 1 and 2.
In a most typical case where a solid is disposed in the gap between the two reflection surfaces 1 and 2, the etalon is formed by two confronting boundary surfaces between the solid and external air.
On the other hand, in a most typical case where a gas is disposed in the gap between the two reflection surfaces 1 and 2, the gas is sealed within a box made of transparent plates made of glass or the like, and the etalon is formed by two confronting boundary surfaces between the gas and the transparent box (transparent plates).
In the conventional etalon, an incident light which is input to the first reflection surface 1 undergoes multiple reflection in the gap between the first and second reflection surfaces 1 and 2, and is output from the second reflection surface 2. A wavelength selection characteristic is realized by utilizing a light transmitted through the second reflection surface 2.
In general, the first and second reflection surfaces 1 and 2 of the etalon do not necessarily have to be parallel to each other, and it is sufficient as long as the first and second reflection surfaces 1 and 2 confront each other.
FIG. 2 is a diagram for explaining the operating principle of the conventional etalon.
In FIG. 2, the etalon is sectioned into three regions 11, 12 and 13 by the first and second reflection surfaces 1 and 2, so that the multiple reflection occurs between the first and second reflection surfaces 1 and 2. For the sake of convenience, it is assumed in FIG. 2 that the first and second reflection surfaces 1 and 2 are parallel to each other, and that the regions 11 and 13 are made of the same material.
In the following description, a wavelength of the incident light to the reflection surface 1 from the region 11 is denoted by λ, an amplitude of this incident light is denoted by a0, an incident angle of the incident light to the reflection surface 1 is denoted by θ, an angle of refraction at the region 12 is denoted by θ′, a refractive index of the material forming the region 11 with respect to light is denoted by n, a refractive index of the material forming the region 12 with respect to light is denoted by n′, an intensity reflectivity at the first reflection surface 1 is denoted by R1, an amplitude reflectivity when incident from the region 11 to the region 12 is denoted by r1, an amplitude reflectivity when incident from the region 12 to the region 11 is denoted by r1′, an amplitude transmittance from the region 11 to the region 12 is denoted by t1, an amplitude transmittance from the region 12 to the region 11 is denoted by t1′, an intensity reflectivity at the second reflection surface 2 is denoted by R2, an amplitude reflectivity when incident from the region 13 to the region 12 is denoted by r2, an amplitude reflectivity when incident from the region 12 to the region 13 is denoted by r2′, an amplitude transmittance from the region 13 to the region 12 is denoted by t2, an amplitude transmittance from the region 12 to the region 13 is denoted by t2′, and a distance between the first and second reflection surfaces 1 and 2 is denoted by h. In addition, a phase error of adjacent lights transmitted or adjacent lights reflected as a result of the multiple reflection is denoted by δ.
FIG. 3 is a diagram for explaining the phase error δ between the adjacent transmitted lights or reflected lights.
A portion of the incident light to the first reflection surface 1 at the incident angle θ is reflected by a reflection angle θ at an incident point Q and becomes LR1. Another portion of the incident light is transmitted to the region 12 at a refraction angle θ′ and a portion of the transmitted light is reflected at a point R on the second reflection surface 2 with a reflection angle θ′. Another portion of the transmitted light is transmitted to the region 13 at a refraction angle θ and becomes LT1.
In addition, the light reflected by the second reflection surface 2 reaches a point S on the first reflection surface 1. A portion of the light reaching the point S is transmitted to the region 11 with a refraction angle θ and becomes LR2, and another portion of the light reaching the point S is reflected by a reflection angle θ′ and reaches a point T on the second reflection surface 2. A portion of the light reaching the point T is transmitted to the region 13 with a refraction angle θ and becomes LT2.
If an intersection of a normal to the reflected light LR1 from the point S is denoted by U, and a normal to the transmitted light LT1 from the point T is denoted by V, a difference in the distances of LR1 and LR2 can be obtained by subtracting the length of a line QU from a sum of the lengths of the lines QR and RS. In addition, a difference in the distances of LT1 and LT2 can be obtained by subtracting the length of a line RV from a sum of the lengths of the lines RS and ST. When the analysis is made based on the precondition that the first and second reflection surfaces 1 and 2 are parallel to each other, the following formula (1) stands, although a description on the calculation details will be omitted.λ=(4πn′h·cos θ′)/λ  (1)
If an amplitude of the transmitted light from the second reflection surface 2 is denoted by at, the following formula (2) stands, where i=√{square root over ( )}(−1).                                                                         a                t                            =                            ⁢                                                                    a                    0                                    ⁢                                      t                    1                                    ⁢                                      t                    2                    ′                                                  +                                                      a                    0                                    ⁢                                      t                    1                                    ⁢                                                            t                      2                      ′                                        ⁡                                          (                                                                        r                          1                          ′                                                ⁢                                                  r                          2                          ′                                                                    )                                                        ⁢                                      exp                    ⁡                                          (                                              ⅈ                        ⁢                                                                                                   ⁢                        δ                                            )                                                                      +                                                                                                      ⁢                                                                    a                    0                                    ⁢                                      t                    1                                    ⁢                                                                                    t                        2                        ′                                            ⁡                                              (                                                                              r                            1                            ′                                                    ⁢                                                      r                            2                            ′                                                                          )                                                              2                                    ⁢                                                            exp                      (                                                                                           ⁢                      ⅈδ                      )                                        2                                                  +                                                                                                      ⁢                                                                    a                    0                                    ⁢                                      t                    1                                    ⁢                                                                                    t                        2                        ′                                            ⁡                                              (                                                                              r                            1                            ′                                                    ⁢                                                      r                            2                            ′                                                                          )                                                              3                                    ⁢                                                            exp                      (                                                                                           ⁢                      ⅈδ                      )                                        3                                                  +                                                                        (        2        )            
As may be seen from the formula (2) above, at is a geometric series of the first term a0t1t2′ and a ratio (r1′r2′)exp(iδ). Hence, the following formula (3) can be obtained from a sum of the series.at=a0t1t2′/{1−(r1′r2′)exp(iδ)}  (3)
Accordingly, an intensity transmittance T of the etalon can be obtained from the following formula (4).
 T=(t1t2′)2/{1−(r1′r2′)2+4r1′r2′ sin2(δ/2)}  (4)
From the law of refraction, the relationships of the following formulas (5) and (6) stand.n sin θ=n′ sin θ′  (5)                                                                        t                1                            ⁢                              t                1                ′                                      =                          1              -                              r                1                2                                              ,                                    r              1              ′                        =                          -                              r                1                                              ,                                    R              1                        =                          r              1              2                                      ⁢                                  ⁢                                                            t                2                            ⁢                              t                2                ′                                      =                          1              -                              r                2                2                                              ,                                    r              2              ′                        =                          -                              r                2                                              ,                                    R              2                        =                          r              2              2                                                          (        6        )            
Therefore, by setting R1=R2=R based on the precondition that the regions 11 and 13 are made of the same material, the relationships (t1t2′)2=(1−R)2, (1−r1′r2′)2=(1−R)2, and r1′r2′=R stand.
Accordingly, an intensity transmittance TE of the etalon can be obtained from the following formula (7).TE=1/{1+4R sin2(δ/2)/(1−R)2}  (7)
FIG. 4 is a diagram showing an example of the intensity transmittance of the conventional etalon for a case where n=1.5, h=1 mm), θ=0 (degrees) and R=0.9. In other words, this intensity transmittance has peaks at approximately 0.8 nm intervals in the narrow wavelength region, and the wavelength selection characteristic of the etalon can be confirmed.
FIG. 5 is a diagram showing a structure of a conventional external resonance type laser.
The external resonance type laser shown in FIG. 5 includes a laser medium 4, a collimator lens 5 for forming a light emitted from the laser medium 4 into a parallel light, a wavelength selection element 6, and a reflection mirror 7. The wavelength selection element 6 feeds back the light having a specific wavelength to the laser medium 4, depending on an incident angle of the light received from the collimator lens 5 and an incident angle of the light reflected from the reflection mirror 7. In FIG. 5, L0 denotes an oscillation light having the specific wavelength.
Normally, a diffraction grating is used as the wavelength selection element 6.
As shown in FIG. 4, it is possible to confirm the wavelength selection characteristic of the transmitted light from the conventional etalon. However, in order to obtain the transmitted light having the wavelength selection characteristic at the light incident side of the etalon, the conventional etalon must be additionally provided with a reflection mirror.
FIG. 6 is a diagram showing an optical system which obtains a light having the wavelength selection characteristic using reflection.
The optical system shown in FIG. 6 includes an etalon 21, a lens 22, and a reflection mirror 23. Of the light incident to the left side of the etalon 21 in FIG. 6, the light portion which undergoes multiple reflection in the etalon 21 is transmitted to the right side of the etalon 21. The transmitted light portion from the right side of the etalon 21 is converged by the lens 22 and is reflected by the reflection mirror 23. The reflected light portion from the reflection mirror 23 is again converged by the lens 22 and is incident to the right side of the etalon 21 so as to be output from the right side of the etalon 21.
Therefore, the light portion which is incident to the right side of the etalon 21, undergoes the multiple reflection in the etalon 21, and is transmitted to the right side of the etalon 21, has the wavelength selection characteristic described above. Hence, when this transmitted light portion from the right side of the etalon 21 is converged by the lens 23, reflected by the reflection mirror 23, again converged by the lens 23, and incident to the right side of the etalon 21, the transmitted light obtained from the left side of the etalon 21 also has the wavelength selection characteristic. Hence, it is possible to obtain the light having the wavelength selection characteristic at the light incident side of the etalon 21 by employing the structure shown in FIG. 6.
However, when reflecting the light transmitted through the etalon 21 by the reflection mirror 23 so as to output the transmitted light from the light incident side of the etalon 21, the reflection mirror 23 cannot make contiguous contact with the etalon 21. This is because the transmitted light having the wavelength selection characteristic cannot be obtained if the reflection mirror 23 were arranged to make contiguous contact with the etalon 21.
Consequently, new problems occur because of the need to arrange the reflection mirror 23 and the etalon 21 separate from each other.
A first problem is that a second etalon which is different from the etalon 21 is formed between the reflection surface at the transmitting side of the etalon 21 and the reflection surface of the reflection mirror 23, if the reflection surface at the transmitting side of the etalon 21 and the reflection surface of the reflection mirror 23 are arranged parallel to each other. In this case, a composite etalon will be formed by the etalon 21 and the second etalon, and the combined wavelength selection characteristic becomes different from the wavelength selection characteristic obtained solely by the etalon 21.
In order to eliminate this first problem, it is necessary to set an angle α formed by the reflection surface at the transmitting side of the etalon 21 and the reflection surface of the reflection mirror 23 to a non-zero value. In addition, in order not to change the wavelength selection characteristic of the light transmitted through the etalon 21 and obtained at the left side of the etalon 21 in FIG. 6, the light converged by the lens 22 must be incident perpendicularly to the reflection surface of the reflection mirror 23. This means that the incident angle θ of the light to the etalon 21 is non-zero, and that the refraction angle θ′ within the etalon 21 is non-zero.
In the formula (1) described above, δ determines the wavelength selection characteristic of the etalon 21. Accordingly, the following formula (8) can be obtained by differentiating the formula (1) by θ′.∂δ/∂θ′=−4πn′h sin θ′/λ  (8)
Since the angle θ′ is normally in a range of 0 to 90 degrees, the formula (8) indicates that the larger the angle θ′, the larger the change in the corresponding δ. Accordingly, the stability of the wavelength selection characteristic of the transmitted light from the etalon 21 deteriorates as the angle θ′ becomes larger.
In other words, the following problems (A) and (B) occur according to the optical system having the structure shown in FIG. 6.
(A) The angle α must be non-zero in order to prevent formation of the composite etalon, thereby causing the structure of the optical system to become complicated.
(B) The light incident angle to the etalon 21 must be non-zero in order to maintain the wavelength selection characteristic of the etalon 21, thereby causing the stability of the wavelength selection characteristic to deteriorate.
The above described problems (A) and (B) are generated due to the combination of the etalon and the reflection mirror. For this reason, it is conceivable to use the reflected light of the etalon itself, but this in turn would cause a second problem.
An intensity reflectivity RE of the reflected light of the etalon itself has a relationship with the intensity transmittance TE described by the following formula (9).Rε=1−TE  (9)
FIG. 7 is a diagram showing an example of the intensity reflectivity of the conventional etalon for a case where n=1.5, h=1 (mm), θ=0 (degrees) and R=0.9. In other words, this intensity reflectivity has valleys at approximately 0.8 nm intervals in the narrow wavelength region, but the reflected light is output with a high reflectivity at virtually all wavelength regions, and the wavelength selection characteristic cannot be obtained.
In other words, if the reflection mirror is not used and the reflected light of the etalon itself is used, it is impossible to obtain the light having the wavelength selection characteristic.
The external resonance type laser having the structure shown in FIG. 5 uses the diffraction grating as the wavelength selection element 6. The light reflected by the diffraction grating is reflected by the reflection mirror 7 and returned to the diffraction grating, so as to feed back the light having the specific wavelength to the laser medium 4 and cause oscillation at the specific wavelength. Hence, the optical system of the external resonance type laser which uses the diffraction grating as the wavelength selection element 6 cannot be formed linearly, that is, elements forming the laser cannot be arranged linearly, and there is a problem in that the structure of the optical system becomes complicated.
In addition, if the etalon using the reflection mirror as shown in FIG. 6 is used as the wavelength selection element, the optical system can be made slightly more linear than the external resonance type laser shown in FIG. 5, but it is still impossible to considerably simplify the structure of the optical system.